We are just going to have to agree to disagree on this one....The key thing here is "alledged". 153 of them didn't do what they were accused of. You see, I don't think you CAN fix all the problems with 100% of certainty. Not as long as you have human beings in the mix. So given that, you should never, ever have a penalty that cannot be undone once carried out... On top of that, it has no deterrent value and is ridiculously expensive.
I am also uncertain about your statistics (153 wrongful executions, out of a pool of 1300-something) - some quick Googling and Wiki-review seems to indicate a considerably lower number (4% wrongful executions rather than 10%, and most of that in decades past), but I won't quibble about it here overly much.
And, I agree that the system cannot be fixed with 100% certainty, but, one of the areas where you and I disagree is that I hold that one does not need to fix it to the 100% certainty level - merely to greatly improve upon existing (or recent decades, more accurately) performance, in order to render the concept viable again.
We disagree about ethics in this context, and we've already been over the cost issue - which can be largely remedied with better quality control on the front end, thereby trimming years or even decades off the lead-time to execution - and most other aspects of the subject matter.
We do, however, agree about the so-called Deterrence Value of Capital Punishment.
I don't think it does very much to deter murder, treason, desertion, etc. - at least not to an extent that could be defended as statistically significant.
What it does do - in the case of murder - is to take vengeance out of the hands of the family and put it into the better-controlled and objective hands of The State.
Otherwise, we would have a never-ending and broad range of multi-generational Hatfields-and-McCoys scenarios playing-out around the country.
We can delude our modern selves all we like, that the Capital Punishment aspect of our criminal justice system, is not about 'vengeance', but that's mere denial.
In the European tradition - stretching back all the way to late tribal and early nation-state times - the Temporal Lord (warlord, chieftain, knight, duke, count, king, emperor, grand poobah, whatever) took for himself the right to try capital cases, in his court, rather than letting the peasantry engage in perpetual vendetta.
Other parts of the world oftentimes developed a criminal trial process for capital cases in much the same way, plus or minus a variation here and there.
As far removed (in time and space) as we are from those earlier times, and as much as we would like to believe that we are sufficiently above such base and savage behaviors, the truth is, that, underlying our modern capital case criminal processes, the State-as-Avenger role is alive and well and merely repackaged.
A murderer takes the life of another human being - considered throughout time one of (if not the) worst crime known to Man.
Having deprived someone else of their life, society empowers The State to avenge the victim by depriving the killer of his-or-her life, in turn.
This is as much about satisfying an ancient human need for vengeance - in a reasonably fair and controlled manner - as anything of a higher nature.
Or so it seems to this observer.